A note on directly ordered subspaces of $\mathbb R^{\small{n}}$
Del Valle, Jennifer ; Wojciechowski, Piotr J.
Tatra Mountains Mathematical Publications, Tome 51 (2012), / Harvested from Mathematical Institute
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Presented is a comprehensive method of determining if a subspace of usually ordered space Rn is directly-ordered. Also, it is proven in an elementary way that if a directly-ordered vector space has a positive cone generated by its extreme vectors then the Riesz Decomposition Property implies the lattice conditions. In particular every directly-ordered subspace of Rn is a lattice-subspace if and only if it satisfies the Riesz Decomposition Property.

Publié le : 2012-01-01
DOI : https://doi.org/10.2478/tatra.v52i0.162 
@article{162,
     title = {A note on directly ordered subspaces of $\mathbb R^{\small{n}}$},
     journal = {Tatra Mountains Mathematical Publications},
     volume = {51},
     year = {2012},
     doi = {10.2478/tatra.v52i0.162},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/162}
}

Del Valle, Jennifer; Wojciechowski, Piotr J. A note on directly ordered subspaces of $\mathbb R^{\small{n}}$. Tatra Mountains Mathematical Publications, Tome 51 (2012) . doi : 10.2478/tatra.v52i0.162. http://gdmltest.u-ga.fr/item/162/